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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A Bayesian Approach for Statistical–Physical Bulk Parameterization of Rain Microphysics. Part I: Scheme Description

A novel framework is proposed for the bulk parameterization of rain microphysics: the Bayesian Observationally Constrained Statistical–Physical Scheme (BOSS). It is designed to facilitate direct constraint by observations using Bayesian inference. BOSS combines existing process-level microphysical knowledge with flexible process rate formulations and parameters constrained by observations within a Bayesian framework. Furthermore, using a raindrop size distribution (DSD) normalization method that relates DSD moments to one another via generalized power series, generalized multivariate power expressions are derived for the microphysical process rates as functions of a set of prognostic DSD moments. The scheme is flexible and can utilize any number and combination of prognostic moments and any number of terms in the process rate formulations. This means that both uncertainty in parameter values and structural uncertainty associated with the process rate formulations can be investigated systematically, which is not possible using traditional schemes. In this paper, BOSS is compared to two- and three-moment versions of a traditional bulk rain microphysics scheme (denoted as MORR). It is demonstrated that some process formulations in MORR are analytically equivalent to the generalized power expressions in BOSS using one or two terms, while others are not. BOSS is able to replicate the behavior of MORR in idealized one-dimensional rainshaft tests, but with a much more flexible and systematic design. Part II of this study describes the application of BOSS to derive rain microphysical process rates and posterior parameter distributions in Bayesian experiments using Markov chain Monte Carlo sampling constrained by synthetic observations.

58 GEOSCIENCES↗
DOE OSTI2021

The dependence of the gradients of oxygen and nitrogen-to-oxygen on stellar age in MaNGA galaxies

For this work, we derived the oxygen abundance (O/H), the nitrogen-to-oxygen (N/O) abundance ratio, and their corresponding radial gradients for a sample of 1431 galaxies from the MaNGA DR15 survey using two different realisations of the strong line method: empirical R calibration and the Bayesian model-based HII-CHI-MISTRY (HCM) code. We find that both abundance calculation methods reveal a correlation between the O/H gradient and the stellar mass of a galaxy. This relation is non-linear, with the steepest average gradients in the intermediate mass range and flatter average gradients for high- and low-mass galaxies. The relation between the N/O gradient and the stellar mass is, on average, non-linear with the steepest gradients in the intermediate mass range (log(M/M ⊙ )~10), flatter gradients for high-mass galaxies, and the flattest gradients for low-mass galaxies. However, the general trend of steepening N/O gradients for higher masses, as reported in previous studies, remains evident. We find a dependence between the O/H and N/O gradients and the galaxy mean stellar age traced by the D(4000) index. For galaxies of lower masses, both gradients are, generally, steeper for intermediate values of D(4000) and flatter for low and high values of D(4000). Only the most massive galaxies do not show this correlation. We interpret this behaviour as an evolution of the metallicity gradients with the age of stellar population. Though the galaxies with a positive slope of the D(4000) radial gradient tend to have flatter O/H and N/O gradients, as compared to those with a negative D(4000) gradient.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Data from: Comparing traditional and Bayesian approaches to ecological meta-analysis

Despite the wide application of meta-analysis in ecology, some of the traditional methods used for meta-analysis may not perform well given the type of data characteristic of ecological meta-analyses. We reviewed published meta-analyses on the ecological impacts of global climate change, evaluating the number of replicates used in the primary studies (ni) and the number of studies or records (k) that were aggregated to calculate a mean effect size. We used the results of the review in a simulation experiment to assess the performance of conventional frequentist and Bayesian meta-analysis methods for estimating a mean effect size and its uncertainty interval. Our literature review showed that ni and k were highly variable, distributions were right-skewed, and were generally small (median ni =5, median k=44). Our simulations show that the choice of method for calculating uncertainty intervals was critical for obtaining appropriate coverage (close to the nominal value of 0.95). When k was low (<40), 95% coverage was achieved by a confidence interval based on the t-distribution that uses an adjusted standard error (the Hartung-Knapp-Sidik-Jonkman, HKSJ), or by a Bayesian credible interval, whereas bootstrap or z-distribution confidence intervals had lower coverage. Despite the importance of the method to calculate the uncertainty interval, 39% of the meta-analyses reviewed did not report the method used, and of the 61% that did, 94% used a potentially problematic method, which may be a consequence of software defaults. In general, for a simple random-effects meta-analysis, the performance of the best frequentist and Bayesian methods were similar for the same combinations of factors (k and mean replication), though the Bayesian approaches had higher than nominal (>95%) coverage for the mean effect when k was very low (k<15). Our literature review suggests that many meta-analyses that used z-distribution or bootstrapping confidence intervals may have over-estimated the statistical significance of their results when the number of studies was low; more appropriate methods need to be adopted in ecological meta-analyses.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2011

Markov Chain Monte Carlo Bayesian Learning for Neural Networks

Conventional training methods for neural networks involve starting al a random location in the solution space of the network weights, navigating an error hyper surface to reach a minimum, and sometime stochastic based techniques (e.g., genetic algorithms) to avoid entrapment in a local minimum. It is further typically necessary to preprocess the data (e.g., normalization) to keep the training algorithm on course. Conversely, Bayesian based learning is an epistemological approach concerned with formally updating the plausibility of competing candidate hypotheses thereby obtaining a posterior distribution for the network weights conditioned on the available data and a prior distribution. In this paper, we developed a powerful methodology for estimating the full residual uncertainty in network weights and therefore network predictions by using a modified Jeffery's prior combined with a Metropolis Markov Chain Monte Carlo method.

Goodrich, Michael S.↗
DOE OSTI2022

Multi-variance replica exchange SGMCMC for inverse and forward problems via Bayesian PINN

Physics-informed neural network (PINN) has been successfully applied in solving a variety of nonlinear non-convex forward and inverse problems. However, the training is challenging because of the non-convex loss functions and the multiple optima in the Bayesian inverse problem. In this work, we propose a multi-variance replica exchange stochastic gradient Langevin dynamics method to tackle the challenge of the multiple local optima in the optimization and the challenge of the multiple modal posterior distribution in the inverse problem. Replica exchange methods are capable of escaping from the local traps and accelerating the convergence; two chains with different temperatures are designed where the low temperature chain aims for the local convergence, and the target of the high temperature chain is to travel globally and explore the whole loss function entropy landscape. However, it may not be efficient to solve mathematical inversion problems by using the vanilla replica method directly since the method doubles the computational cost in evaluating the forward solvers (likelihood functions) in the two chains. To address this issue, we propose to make different assumptions on the energy function estimation and this facilities one to use solvers of different fidelities in the likelihood function evaluation. More precisely, one can use a solver with low fidelity in the high temperature chain while using a solver with high fidelity in the low temperature chain. Our proposed method significantly lowers the computational cost in the high temperature chain, meanwhile preserving the accuracy and converging very fast. Here we give an unbiased estimate of the swapping rate and give an estimation of the discretization error of the scheme. To verify our idea, we design and solve four inverse problems which have multiple modes. The proposed method is also employed to train the Bayesian PINN to solve the forward and inverse problems; faster and more accurate convergence has been observed when compared to the stochastic gradient Langevin dynamics (SGLD) method and vanilla replica exchange methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Dynamic, risk informed decision support systems and methods

The present disclosure is directed to a decision support system or tool based on a Bayesian Network (BN) framework. The diagnostic support tool is created by using advanced Probabilistic Risk Assessment (PRA) method(s) to construct Bayesian Networks (BNs) that form a Bayesian Decision Support Process (BDSP) to provide science-based decision support for understanding and managing events in complex systems. In an embodiment, the PRA method(s) may include Discrete Dynamic Event Trees (DDETs) and simulations.

Groth, Katrina↗
DOE OSTI2023

Bayesian High-Rank Hankel Matrix Completion for Nonlinear Synchrophasor Data Recovery

Phasor measurement units (PMUs) provide high temporal-resolution synchrophasor measurements for power system monitoring and control. The frequent data quality issues, such as missing and bad data, prevent the incorporation of synchrophasor data in real-time operations. Most existing data-driven data recovery methods assume the power system dynamics can be approximated by a linear dynamical system, and the recovery performance degrades significantly when the power system is experiencing nonlinear dynamics during significant events. Here, this paper proposes a data-driven Bayesian nonlinear synchrophasor data recovery method (Ba-NSDR) that can recover a consecutive time period of simultaneous data losses or errors across all channels, even when the underlying system is highly nonlinear. The idea is to lift the Hankel matrix of the spatial-temporal synchrophasor data to a higher dimension such that the lifted Hankel matrix is low-rank in that space and can be processed with the kernel trick. Our proposed Bayesian method then infers the probabilistic distributions of synchrophasor from the partial observations. Some distinctive features of Ba-NSDR include an uncertainty index to measure the accuracy of the recovery result and the robustness to parameter selections. Our method is verified on both synthetic and recorded event datasets.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Bayesian estimation of cross-section and errors of experiment and calculation for accurate prediction of neutronic characteristics

In some experiments, there might be a correlation of experimental errors such as an error caused by fabrication. The correlation of calculation errors also might exist among analyses of experiments. In the present study, considering these correlations, the cross-section and errors of experiment and calculation are adjusted for the accurate prediction of neutronic characteristics. The adjustment method is derived based on Bayesian theory. The 'a posteriori' distributions of cross-section and errors of experiment and calculation are obtained by the derivation. The case study is performed by using the benchmarks of light-water moderated experiments reported in ICSBEP. The error from fuel rod fabrication and measurement are included in the experiment error, and the error from the simplification of the benchmark model is included in the calculation error. Since these errors have a positive correlation among the benchmarks, the prediction accuracy is expected to be improved by considering these correlations. For the sensitivity analysis of the correlation among benchmarks, the correlation coefficient of experiment error and that of calculation error is assumed from 0.0 to 0.9. The results indicate that the prediction accuracy of the multiplication factor can be improved by increasing the correlation coefficient of experiment error and that of calculation error. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Technical Report for Bayesian Optimization and Reinforcement Learning for Beam Polarization Increase in the BNL Hadron Injectors

This project developed and evaluated physics-informed Bayesian learning and machine learning (ML)-based optimization methods for improving beam polarization preservation in the BNL hadron injector chain. The work focused on uncertainty-aware digital twin modeling, Bayesian calibration of accelerator simulations using beam measurements, and data-efficient optimization strategies including Bayesian optimization and reinforcement learning. These methods were applied to injector tuning and RF control problems in realistic accelerator settings to support improved operational robustness and readiness for RHIC operations and future Electron–Ion Collider facilities. No subject inventions were disclosed under this award.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Accelerating Hamiltonian Monte Carlo for Bayesian inference in neural networks and neural operators

Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high dimensionality of the network’s parameter space and the non-convexity of their posterior distributions. Therefore, various approximation techniques, such as variational inference (VI) or stochastic gradient MCMC, are often employed to infer the posterior distribution of the network parameters. Such approximations introduce inaccuracies in the inferred distributions, resulting in unreliable uncertainty estimates. In this work, we propose a hybrid approach that combines inexpensive VI and accurate HMC methods to efficiently and accurately quantify uncertainties in neural networks and neural operators. The proposed approach leverages an initial VI training on the full network. We examine the influence of individual parameters on the prediction uncertainty, which shows that a large proportion of the parameters do not contribute substantially to uncertainty in the network predictions. This information is then used to significantly reduce the dimension of the parameter space, and HMC is performed only for the subset of network parameters that strongly influence prediction uncertainties. This yields a framework for accelerating the full batch HMC for posterior inference in neural networks. We demonstrate the efficiency and accuracy of the proposed framework on deep neural networks and operator networks, showing that inference can be performed for large networks with tens to hundreds of thousands of parameters. Finally, we show that this method can effectively learn surrogates for complex physical systems by modeling the operator that maps from upstream conditions to wall-pressure data on a cone in hypersonic flow.

Bayesian inference↗
DOE OSTI2022

Inference, Prediction, & Entropy-Rate Estimation of Continuous-Time, Discrete-Event Processes

Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide new methods for inferring, predicting, and estimating them. The methods rely on an extension of Bayesian structural inference that takes advantage of neural network’s universal approximation power. Based on experiments with complex synthetic data, the methods are competitive with the state-of-the-art for prediction and entropy-rate estimation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Bayesian analysis for estimating statistical parameter distributions of elasto-viscoplastic material models

High temperature design methods rely on constitutive models for inelastic deformation and failure typically calibrated against the mean of experimental data without considering the associated scatter. Variability may arise from the experimental data acquisition process, from heat-to-heat material property variations, or both and need to be accurately captured to predict parameter bounds leading to efficient component design. Applying the Bayesian Markov Chain Monte Carlo (MCMC) method to produce statistical models capturing the underlying uncertainty in the experimental data is an area of ongoing research interest. This work varies aspects of the Bayesian MCMC method and explores their effect on the posterior parameter distributions for a uniaxial elasto-viscoplastic damage model using synthetically generated reference data. From our analysis with the uniaxial inelastic model we determine that an informed prior distribution including different types of test conditions results in more accurate posterior parameter distributions. The parameter posterior distributions, however, do not improve when increasing the number of similar experimental data. Additionally, changing the amount of scatter in the data affects the quality of the posterior distributions, especially for the less sensitive model parameters. Moreover, we perform a sensitivity study of the model parameters against the likelihood function prior to the Bayesian analysis. The results of the sensitivity analysis help to determine the reliability of the posterior distributions and reduce the dimensionality of the problem by fixing the insensitive parameters. The comprehensive study described in this work demonstrates how to efficiently apply the Bayesian MCMC methodology to capture parameter uncertainties in high temperature inelastic material models. Quantifying these uncertainties in inelastic models will improve high temperature engineering design practices and lead to safer, more effective component designs.

42 ENGINEERING↗
NASA NTRS2013

Estimating the Properties of Hard X-Ray Solar Flares by Constraining Model Parameters

We wish to better constrain the properties of solar flares by exploring how parameterized models of solar flares interact with uncertainty estimation methods. We compare four different methods of calculating uncertainty estimates in fitting parameterized models to Ramaty High Energy Solar Spectroscopic Imager X-ray spectra, considering only statistical sources of error. Three of the four methods are based on estimating the scale-size of the minimum in a hypersurface formed by the weighted sum of the squares of the differences between the model fit and the data as a function of the fit parameters, and are implemented as commonly practiced. The fourth method is also based on the difference between the data and the model, but instead uses Bayesian data analysis and Markov chain Monte Carlo (MCMC) techniques to calculate an uncertainty estimate. Two flare spectra are modeled: one from the Geostationary Operational Environmental Satellite X1.3 class flare of 2005 January 19, and the other from the X4.8 flare of 2002 July 23.We find that the four methods give approximately the same uncertainty estimates for the 2005 January 19 spectral fit parameters, but lead to very different uncertainty estimates for the 2002 July 23 spectral fit. This is because each method implements different analyses of the hypersurface, yielding method-dependent results that can differ greatly depending on the shape of the hypersurface. The hypersurface arising from the 2005 January 19 analysis is consistent with a normal distribution; therefore, the assumptions behind the three non- Bayesian uncertainty estimation methods are satisfied and similar estimates are found. The 2002 July 23 analysis shows that the hypersurface is not consistent with a normal distribution, indicating that the assumptions behind the three non-Bayesian uncertainty estimation methods are not satisfied, leading to differing estimates of the uncertainty. We find that the shape of the hypersurface is crucial in understanding the output from each uncertainty estimation technique, and that a crucial factor determining the shape of hypersurface is the location of the low-energy cutoff relative to energies where the thermal emission dominates. The Bayesian/MCMC approach also allows us to provide detailed information on probable values of the low-energy cutoff, Ec, a crucial parameter in defining the energy content of the flare-accelerated electrons. We show that for the 2002 July 23 flare data, there is a 95% probability that Ec lies below approximately 40 keV, and a 68% probability that it lies in the range 7-36 keV. Further, the low-energy cutoff is more likely to be in the range 25-35 keV than in any other 10 keV wide energy range. The low-energy cutoff for the 2005 January 19 flare is more tightly constrained to 107 +/- 4 keV with 68% probability.

X-rays↗
NASA NTRS1992

A new method for the detection of a periodic signal of unknown shape and period

A method was developed for the detection and measurement of a periodic signal with unknown characteristics in a data set where the existence of such signal was not known. The method detects a signal by using Bayesian probability theory to compare a constant model for the signal to members of a class of models with periodic structure. The method was applied to simulated data generated with both stepwise and sinusoidal light curves, demonstrating that such signals can be sensitively detected and the signal frequency and its shape can be accurately estimated.

Gregory, P. C.↗
DOE OSTI2025

Autonomous organic synthesis for redox flow batteries via flexible batch Bayesian optimization

Traditional trial-and-error methods for materials discovery are inefficient to meet the urgent demands posed by the rapid progression of climate change. This urgency has driven the increasing interest in integrating robotics and machine learning into materials research to accelerate experimental learning. However, idealized decision-making frameworks to achieve maximum sampling efficiency are not always compatible with high-throughput experimental workflows inside a laboratory. For multi-step chemical processes, differences in hardware capacities can complicate the digital framework by introducing constraints on the maximum number of samples in each step of the experiment, hence causing varying batch sizes in variable selection within the same batch. Therefore, designing flexible sampling algorithms is necessary to accommodate the multi-step synthesis with practical constraints unique to each high-throughput workflow. In this work, we designed and employed three strategies on a high-throughput robotic platform to optimize the sulfonation reaction of redox-active molecules used in flow batteries. Our strategies adapt to the multi-step experimental workflow, where their formulation and heating steps are separate, causing varying batch size requirements. By strategically sampling using clustering and mixed-variable batch Bayesian optimization, we were able to iteratively identify optimal conditions that maximize the yields. Our work presents a flexible approach that allows tailoring the machine learning decision-making to suit the practical constraints in individual high-throughput experimental platforms, followed by performing resource-efficient yield optimization using available open-source Python libraries.

Tamura, Clara [Univ. of Washington, Seattle, WA (U↗
DOE OSTI2020

UQTk User Manual (V.3.1.0)

The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 3.1.0 offers intrusive and non-intrusive methods for propagating input uncertainties through computational models, tools for sensitivity analysis, methods for sparse surrogate construction, and Bayesian inference tools for inferring parameters from experimental data. This manual discusses the download and installation process for UQTk, provides pointers to the UQ methods used in the toolkit, and describes some of the examples provided with the toolkit.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

UQTk Version 3.1.1 User Manual

The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 3.1.1 offers intrusive and non-intrusive methods for propagating input uncertainties through computational models, tools for sensitivity analysis, methods for sparse surrogate construction, and Bayesian inference tools for inferring parameters from experimental data. This manual discusses the download and installation process for UQTk, provides pointers to the UQ methods used in the toolkit, and describes some of the examples provided with the toolkit.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

UQTk Version 3.1.2 User Manual

The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 3.1.2 offers intrusive and non-intrusive methods for propagating input uncertainties through computational models, tools for sensitivity analysis, methods for sparse surrogate construction, and Bayesian inference tools for inferring parameters from experimental data. This manual discusses the download and installation process for UQTk, provides pointers to the UQ methods used in the toolkit, and describes some of the examples provided with the toolkit.

97 MATHEMATICS AND COMPUTING↗